Solve (6x^5)^2*x^2

$$( 6 x ^ { 5 } ) ^ { 2 } \cdot x ^ { 2 }$$

Evaluate

$$36x^{12}$$

Steps for the Product of Two Exponentials

Use the rules of exponents to simplify the expression.

$$\left(6x^{5}\right)^{2}\left(x^{1}\right)^{2}$$

To raise the product of two or more numbers to a power, raise each number to the power and take their product.

$$6^{2}\left(x^{5}\right)^{2}\times 1^{2}\left(x^{1}\right)^{2}$$

Use the Commutative Property of Multiplication.

$$6^{2}\times 1^{2}\left(x^{5}\right)^{2}\left(x^{1}\right)^{2}$$

To raise a power to another power, multiply the exponents.

$$6^{2}\times 1^{2}x^{5\times 2}x^{2}$$

Multiply 5 times 2.

$$6^{2}\times 1^{2}x^{10}x^{2}$$

To multiply powers of the same base, add their exponents.

$$6^{2}\times 1^{2}x^{10+2}$$

Add the exponents 10 and 2.

$$6^{2}\times 1^{2}x^{12}$$

Raise 6 to the power 2.

$$36\times 1^{2}x^{12}$$

Expand

$$36x^{12}$$

Steps for the Product of Two Exponentials

Use the rules of exponents to simplify the expression.

$$\left(6x^{5}\right)^{2}\left(x^{1}\right)^{2}$$

To raise the product of two or more numbers to a power, raise each number to the power and take their product.

$$6^{2}\left(x^{5}\right)^{2}\times 1^{2}\left(x^{1}\right)^{2}$$

Use the Commutative Property of Multiplication.

$$6^{2}\times 1^{2}\left(x^{5}\right)^{2}\left(x^{1}\right)^{2}$$

To raise a power to another power, multiply the exponents.

$$6^{2}\times 1^{2}x^{5\times 2}x^{2}$$

Multiply 5 times 2.

$$6^{2}\times 1^{2}x^{10}x^{2}$$

To multiply powers of the same base, add their exponents.

$$6^{2}\times 1^{2}x^{10+2}$$

Add the exponents 10 and 2.

$$6^{2}\times 1^{2}x^{12}$$

Raise 6 to the power 2.

$$36\times 1^{2}x^{12}$$